Properties

Label 288.3.u.a.91.5
Level $288$
Weight $3$
Character 288.91
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 91.5
Character \(\chi\) \(=\) 288.91
Dual form 288.3.u.a.19.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.360897 + 1.96717i) q^{2} +(-3.73951 + 1.41989i) q^{4} +(0.452310 + 0.187353i) q^{5} +(0.429965 - 0.429965i) q^{7} +(-4.14274 - 6.84381i) q^{8} +O(q^{10})\) \(q+(0.360897 + 1.96717i) q^{2} +(-3.73951 + 1.41989i) q^{4} +(0.452310 + 0.187353i) q^{5} +(0.429965 - 0.429965i) q^{7} +(-4.14274 - 6.84381i) q^{8} +(-0.205317 + 0.957385i) q^{10} +(-17.3350 - 7.18039i) q^{11} +(-19.9596 + 8.26755i) q^{13} +(1.00099 + 0.690640i) q^{14} +(11.9678 - 10.6194i) q^{16} +13.5961i q^{17} +(-3.45810 - 8.34859i) q^{19} +(-1.95744 - 0.0583763i) q^{20} +(7.86888 - 36.6922i) q^{22} +(16.8850 + 16.8850i) q^{23} +(-17.5082 - 17.5082i) q^{25} +(-23.4670 - 36.2802i) q^{26} +(-0.997353 + 2.21836i) q^{28} +(-13.8385 - 33.4091i) q^{29} -24.5614i q^{31} +(25.2093 + 19.7102i) q^{32} +(-26.7458 + 4.90679i) q^{34} +(0.275033 - 0.113922i) q^{35} +(9.89595 + 4.09904i) q^{37} +(15.1751 - 9.81565i) q^{38} +(-0.591598 - 3.87168i) q^{40} +(-14.4867 + 14.4867i) q^{41} +(17.8494 + 7.39348i) q^{43} +(75.0197 + 2.23730i) q^{44} +(-27.1219 + 39.3094i) q^{46} -43.6087 q^{47} +48.6303i q^{49} +(28.1229 - 40.7602i) q^{50} +(62.9001 - 59.2571i) q^{52} +(-28.0630 + 67.7501i) q^{53} +(-6.49552 - 6.49552i) q^{55} +(-4.72383 - 1.16136i) q^{56} +(60.7270 - 39.2799i) q^{58} +(-1.70130 + 4.10730i) q^{59} +(3.53360 + 8.53087i) q^{61} +(48.3165 - 8.86416i) q^{62} +(-29.6753 + 56.7043i) q^{64} -10.5769 q^{65} +(-0.300169 + 0.124334i) q^{67} +(-19.3050 - 50.8427i) q^{68} +(0.323363 + 0.499921i) q^{70} +(29.0914 - 29.0914i) q^{71} +(-68.2273 + 68.2273i) q^{73} +(-4.49208 + 20.9463i) q^{74} +(24.7857 + 26.3095i) q^{76} +(-10.5408 + 4.36612i) q^{77} +67.7588 q^{79} +(7.40274 - 2.56105i) q^{80} +(-33.7260 - 23.2695i) q^{82} +(16.4008 + 39.5950i) q^{83} +(-2.54727 + 6.14965i) q^{85} +(-8.10241 + 37.7811i) q^{86} +(22.6733 + 148.384i) q^{88} +(45.3745 + 45.3745i) q^{89} +(-5.02718 + 12.1367i) q^{91} +(-87.1165 - 39.1667i) q^{92} +(-15.7383 - 85.7857i) q^{94} -4.42403i q^{95} -119.312 q^{97} +(-95.6639 + 17.5505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.360897 + 1.96717i 0.180449 + 0.983584i
\(3\) 0 0
\(4\) −3.73951 + 1.41989i −0.934877 + 0.354973i
\(5\) 0.452310 + 0.187353i 0.0904620 + 0.0374706i 0.427456 0.904036i \(-0.359410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(6\) 0 0
\(7\) 0.429965 0.429965i 0.0614236 0.0614236i −0.675728 0.737151i \(-0.736170\pi\)
0.737151 + 0.675728i \(0.236170\pi\)
\(8\) −4.14274 6.84381i −0.517843 0.855476i
\(9\) 0 0
\(10\) −0.205317 + 0.957385i −0.0205317 + 0.0957385i
\(11\) −17.3350 7.18039i −1.57591 0.652763i −0.588149 0.808752i \(-0.700143\pi\)
−0.987759 + 0.155990i \(0.950143\pi\)
\(12\) 0 0
\(13\) −19.9596 + 8.26755i −1.53536 + 0.635965i −0.980595 0.196044i \(-0.937190\pi\)
−0.554761 + 0.832010i \(0.687190\pi\)
\(14\) 1.00099 + 0.690640i 0.0714991 + 0.0493315i
\(15\) 0 0
\(16\) 11.9678 10.6194i 0.747988 0.663712i
\(17\) 13.5961i 0.799770i 0.916565 + 0.399885i \(0.130950\pi\)
−0.916565 + 0.399885i \(0.869050\pi\)
\(18\) 0 0
\(19\) −3.45810 8.34859i −0.182005 0.439399i 0.806374 0.591405i \(-0.201427\pi\)
−0.988380 + 0.152006i \(0.951427\pi\)
\(20\) −1.95744 0.0583763i −0.0978718 0.00291881i
\(21\) 0 0
\(22\) 7.86888 36.6922i 0.357677 1.66783i
\(23\) 16.8850 + 16.8850i 0.734131 + 0.734131i 0.971435 0.237304i \(-0.0762639\pi\)
−0.237304 + 0.971435i \(0.576264\pi\)
\(24\) 0 0
\(25\) −17.5082 17.5082i −0.700327 0.700327i
\(26\) −23.4670 36.2802i −0.902579 1.39539i
\(27\) 0 0
\(28\) −0.997353 + 2.21836i −0.0356197 + 0.0792271i
\(29\) −13.8385 33.4091i −0.477190 1.15204i −0.960921 0.276821i \(-0.910719\pi\)
0.483732 0.875216i \(-0.339281\pi\)
\(30\) 0 0
\(31\) 24.5614i 0.792305i −0.918185 0.396152i \(-0.870345\pi\)
0.918185 0.396152i \(-0.129655\pi\)
\(32\) 25.2093 + 19.7102i 0.787790 + 0.615944i
\(33\) 0 0
\(34\) −26.7458 + 4.90679i −0.786642 + 0.144317i
\(35\) 0.275033 0.113922i 0.00785807 0.00325492i
\(36\) 0 0
\(37\) 9.89595 + 4.09904i 0.267458 + 0.110785i 0.512382 0.858757i \(-0.328763\pi\)
−0.244924 + 0.969542i \(0.578763\pi\)
\(38\) 15.1751 9.81565i 0.399344 0.258306i
\(39\) 0 0
\(40\) −0.591598 3.87168i −0.0147899 0.0967919i
\(41\) −14.4867 + 14.4867i −0.353334 + 0.353334i −0.861348 0.508015i \(-0.830380\pi\)
0.508015 + 0.861348i \(0.330380\pi\)
\(42\) 0 0
\(43\) 17.8494 + 7.39348i 0.415103 + 0.171941i 0.580453 0.814294i \(-0.302875\pi\)
−0.165350 + 0.986235i \(0.552875\pi\)
\(44\) 75.0197 + 2.23730i 1.70499 + 0.0508477i
\(45\) 0 0
\(46\) −27.1219 + 39.3094i −0.589607 + 0.854553i
\(47\) −43.6087 −0.927845 −0.463922 0.885876i \(-0.653558\pi\)
−0.463922 + 0.885876i \(0.653558\pi\)
\(48\) 0 0
\(49\) 48.6303i 0.992454i
\(50\) 28.1229 40.7602i 0.562458 0.815204i
\(51\) 0 0
\(52\) 62.9001 59.2571i 1.20962 1.13956i
\(53\) −28.0630 + 67.7501i −0.529490 + 1.27830i 0.402367 + 0.915478i \(0.368188\pi\)
−0.931857 + 0.362825i \(0.881812\pi\)
\(54\) 0 0
\(55\) −6.49552 6.49552i −0.118100 0.118100i
\(56\) −4.72383 1.16136i −0.0843541 0.0207386i
\(57\) 0 0
\(58\) 60.7270 39.2799i 1.04702 0.677240i
\(59\) −1.70130 + 4.10730i −0.0288356 + 0.0696153i −0.937641 0.347604i \(-0.886995\pi\)
0.908806 + 0.417219i \(0.136995\pi\)
\(60\) 0 0
\(61\) 3.53360 + 8.53087i 0.0579279 + 0.139850i 0.950193 0.311661i \(-0.100885\pi\)
−0.892266 + 0.451511i \(0.850885\pi\)
\(62\) 48.3165 8.86416i 0.779299 0.142970i
\(63\) 0 0
\(64\) −29.6753 + 56.7043i −0.463677 + 0.886004i
\(65\) −10.5769 −0.162721
\(66\) 0 0
\(67\) −0.300169 + 0.124334i −0.00448013 + 0.00185573i −0.384922 0.922949i \(-0.625772\pi\)
0.380442 + 0.924805i \(0.375772\pi\)
\(68\) −19.3050 50.8427i −0.283897 0.747686i
\(69\) 0 0
\(70\) 0.323363 + 0.499921i 0.00461947 + 0.00714173i
\(71\) 29.0914 29.0914i 0.409738 0.409738i −0.471909 0.881647i \(-0.656435\pi\)
0.881647 + 0.471909i \(0.156435\pi\)
\(72\) 0 0
\(73\) −68.2273 + 68.2273i −0.934620 + 0.934620i −0.997990 0.0633700i \(-0.979815\pi\)
0.0633700 + 0.997990i \(0.479815\pi\)
\(74\) −4.49208 + 20.9463i −0.0607037 + 0.283059i
\(75\) 0 0
\(76\) 24.7857 + 26.3095i 0.326127 + 0.346177i
\(77\) −10.5408 + 4.36612i −0.136893 + 0.0567029i
\(78\) 0 0
\(79\) 67.7588 0.857706 0.428853 0.903374i \(-0.358918\pi\)
0.428853 + 0.903374i \(0.358918\pi\)
\(80\) 7.40274 2.56105i 0.0925342 0.0320131i
\(81\) 0 0
\(82\) −33.7260 23.2695i −0.411292 0.283775i
\(83\) 16.4008 + 39.5950i 0.197600 + 0.477048i 0.991358 0.131186i \(-0.0418784\pi\)
−0.793758 + 0.608234i \(0.791878\pi\)
\(84\) 0 0
\(85\) −2.54727 + 6.14965i −0.0299679 + 0.0723488i
\(86\) −8.10241 + 37.7811i −0.0942140 + 0.439315i
\(87\) 0 0
\(88\) 22.6733 + 148.384i 0.257651 + 1.68618i
\(89\) 45.3745 + 45.3745i 0.509825 + 0.509825i 0.914473 0.404647i \(-0.132606\pi\)
−0.404647 + 0.914473i \(0.632606\pi\)
\(90\) 0 0
\(91\) −5.02718 + 12.1367i −0.0552438 + 0.133370i
\(92\) −87.1165 39.1667i −0.946919 0.425725i
\(93\) 0 0
\(94\) −15.7383 85.7857i −0.167428 0.912614i
\(95\) 4.42403i 0.0465688i
\(96\) 0 0
\(97\) −119.312 −1.23002 −0.615012 0.788518i \(-0.710849\pi\)
−0.615012 + 0.788518i \(0.710849\pi\)
\(98\) −95.6639 + 17.5505i −0.976163 + 0.179087i
\(99\) 0 0
\(100\) 90.3317 + 40.6122i 0.903317 + 0.406122i
\(101\) −98.7914 40.9207i −0.978133 0.405156i −0.164399 0.986394i \(-0.552569\pi\)
−0.813734 + 0.581238i \(0.802569\pi\)
\(102\) 0 0
\(103\) 127.634 127.634i 1.23916 1.23916i 0.278817 0.960344i \(-0.410058\pi\)
0.960344 0.278817i \(-0.0899423\pi\)
\(104\) 139.269 + 102.349i 1.33913 + 0.984130i
\(105\) 0 0
\(106\) −143.404 30.7538i −1.35286 0.290131i
\(107\) −94.9289 39.3208i −0.887186 0.367484i −0.107906 0.994161i \(-0.534415\pi\)
−0.779279 + 0.626677i \(0.784415\pi\)
\(108\) 0 0
\(109\) −27.8610 + 11.5404i −0.255605 + 0.105875i −0.506807 0.862060i \(-0.669174\pi\)
0.251202 + 0.967935i \(0.419174\pi\)
\(110\) 10.4336 15.1220i 0.0948507 0.137473i
\(111\) 0 0
\(112\) 0.579776 9.71170i 0.00517658 0.0867116i
\(113\) 140.786i 1.24590i 0.782263 + 0.622948i \(0.214065\pi\)
−0.782263 + 0.622948i \(0.785935\pi\)
\(114\) 0 0
\(115\) 4.47380 + 10.8007i 0.0389026 + 0.0939193i
\(116\) 99.1864 + 105.284i 0.855055 + 0.907623i
\(117\) 0 0
\(118\) −8.69375 1.86443i −0.0736758 0.0158003i
\(119\) 5.84584 + 5.84584i 0.0491247 + 0.0491247i
\(120\) 0 0
\(121\) 163.384 + 163.384i 1.35028 + 1.35028i
\(122\) −15.5064 + 10.0300i −0.127102 + 0.0822128i
\(123\) 0 0
\(124\) 34.8746 + 91.8477i 0.281247 + 0.740707i
\(125\) −9.32274 22.5071i −0.0745819 0.180057i
\(126\) 0 0
\(127\) 163.979i 1.29117i 0.763687 + 0.645587i \(0.223387\pi\)
−0.763687 + 0.645587i \(0.776613\pi\)
\(128\) −122.257 37.9120i −0.955130 0.296187i
\(129\) 0 0
\(130\) −3.81717 20.8065i −0.0293629 0.160050i
\(131\) 11.2279 4.65074i 0.0857090 0.0355018i −0.339417 0.940636i \(-0.610230\pi\)
0.425126 + 0.905134i \(0.360230\pi\)
\(132\) 0 0
\(133\) −5.07646 2.10274i −0.0381689 0.0158101i
\(134\) −0.352916 0.545611i −0.00263370 0.00407172i
\(135\) 0 0
\(136\) 93.0490 56.3251i 0.684184 0.414155i
\(137\) −21.2983 + 21.2983i −0.155462 + 0.155462i −0.780552 0.625090i \(-0.785062\pi\)
0.625090 + 0.780552i \(0.285062\pi\)
\(138\) 0 0
\(139\) −154.836 64.1351i −1.11393 0.461404i −0.251639 0.967821i \(-0.580969\pi\)
−0.862288 + 0.506418i \(0.830969\pi\)
\(140\) −0.866729 + 0.816529i −0.00619092 + 0.00583235i
\(141\) 0 0
\(142\) 67.7268 + 46.7287i 0.476949 + 0.329076i
\(143\) 405.364 2.83471
\(144\) 0 0
\(145\) 17.7039i 0.122096i
\(146\) −158.838 109.592i −1.08793 0.750627i
\(147\) 0 0
\(148\) −42.8262 1.27720i −0.289366 0.00862971i
\(149\) 90.9258 219.514i 0.610240 1.47325i −0.252497 0.967598i \(-0.581252\pi\)
0.862737 0.505653i \(-0.168748\pi\)
\(150\) 0 0
\(151\) −82.0484 82.0484i −0.543367 0.543367i 0.381147 0.924514i \(-0.375529\pi\)
−0.924514 + 0.381147i \(0.875529\pi\)
\(152\) −42.8101 + 58.2526i −0.281645 + 0.383241i
\(153\) 0 0
\(154\) −12.3930 19.1597i −0.0804742 0.124414i
\(155\) 4.60166 11.1094i 0.0296881 0.0716735i
\(156\) 0 0
\(157\) −52.8906 127.689i −0.336883 0.813307i −0.998011 0.0630341i \(-0.979922\pi\)
0.661129 0.750272i \(-0.270078\pi\)
\(158\) 24.4540 + 133.293i 0.154772 + 0.843627i
\(159\) 0 0
\(160\) 7.70964 + 13.6382i 0.0481853 + 0.0852385i
\(161\) 14.5199 0.0901859
\(162\) 0 0
\(163\) 54.8297 22.7112i 0.336379 0.139333i −0.208099 0.978108i \(-0.566728\pi\)
0.544478 + 0.838775i \(0.316728\pi\)
\(164\) 33.6035 74.7426i 0.204900 0.455747i
\(165\) 0 0
\(166\) −71.9710 + 46.5528i −0.433560 + 0.280439i
\(167\) 98.7296 98.7296i 0.591195 0.591195i −0.346759 0.937954i \(-0.612718\pi\)
0.937954 + 0.346759i \(0.112718\pi\)
\(168\) 0 0
\(169\) 210.533 210.533i 1.24576 1.24576i
\(170\) −13.0167 2.79151i −0.0765688 0.0164207i
\(171\) 0 0
\(172\) −77.2460 2.30369i −0.449105 0.0133936i
\(173\) 6.09221 2.52348i 0.0352151 0.0145866i −0.365006 0.931005i \(-0.618933\pi\)
0.400221 + 0.916418i \(0.368933\pi\)
\(174\) 0 0
\(175\) −15.0558 −0.0860332
\(176\) −283.713 + 98.1534i −1.61201 + 0.557690i
\(177\) 0 0
\(178\) −72.8837 + 105.635i −0.409459 + 0.593454i
\(179\) −80.6673 194.748i −0.450655 1.08798i −0.972073 0.234677i \(-0.924597\pi\)
0.521418 0.853301i \(-0.325403\pi\)
\(180\) 0 0
\(181\) −59.7464 + 144.241i −0.330091 + 0.796910i 0.668493 + 0.743718i \(0.266939\pi\)
−0.998584 + 0.0531918i \(0.983061\pi\)
\(182\) −25.6892 5.50922i −0.141150 0.0302704i
\(183\) 0 0
\(184\) 45.6075 185.508i 0.247867 1.00820i
\(185\) 3.70807 + 3.70807i 0.0200436 + 0.0200436i
\(186\) 0 0
\(187\) 97.6252 235.688i 0.522060 1.26036i
\(188\) 163.075 61.9196i 0.867421 0.329360i
\(189\) 0 0
\(190\) 8.70282 1.59662i 0.0458043 0.00840327i
\(191\) 107.812i 0.564460i −0.959347 0.282230i \(-0.908926\pi\)
0.959347 0.282230i \(-0.0910741\pi\)
\(192\) 0 0
\(193\) −174.830 −0.905855 −0.452927 0.891547i \(-0.649620\pi\)
−0.452927 + 0.891547i \(0.649620\pi\)
\(194\) −43.0595 234.707i −0.221956 1.20983i
\(195\) 0 0
\(196\) −69.0497 181.853i −0.352294 0.927822i
\(197\) 108.472 + 44.9304i 0.550618 + 0.228073i 0.640606 0.767870i \(-0.278683\pi\)
−0.0899887 + 0.995943i \(0.528683\pi\)
\(198\) 0 0
\(199\) 190.347 190.347i 0.956516 0.956516i −0.0425770 0.999093i \(-0.513557\pi\)
0.999093 + 0.0425770i \(0.0135568\pi\)
\(200\) −47.2907 + 192.355i −0.236453 + 0.961773i
\(201\) 0 0
\(202\) 44.8445 209.108i 0.222002 1.03519i
\(203\) −20.3148 8.41467i −0.100073 0.0414516i
\(204\) 0 0
\(205\) −9.26659 + 3.83835i −0.0452029 + 0.0187237i
\(206\) 297.140 + 205.014i 1.44242 + 0.995215i
\(207\) 0 0
\(208\) −151.077 + 310.904i −0.726331 + 1.49473i
\(209\) 169.553i 0.811259i
\(210\) 0 0
\(211\) 86.6725 + 209.246i 0.410770 + 0.991686i 0.984932 + 0.172944i \(0.0553281\pi\)
−0.574162 + 0.818742i \(0.694672\pi\)
\(212\) 8.74400 293.198i 0.0412453 1.38301i
\(213\) 0 0
\(214\) 43.0911 200.932i 0.201360 0.938934i
\(215\) 6.68829 + 6.68829i 0.0311083 + 0.0311083i
\(216\) 0 0
\(217\) −10.5606 10.5606i −0.0486662 0.0486662i
\(218\) −32.7569 50.6423i −0.150261 0.232304i
\(219\) 0 0
\(220\) 33.5130 + 15.0671i 0.152332 + 0.0684869i
\(221\) −112.406 271.373i −0.508626 1.22793i
\(222\) 0 0
\(223\) 103.845i 0.465671i −0.972516 0.232836i \(-0.925200\pi\)
0.972516 0.232836i \(-0.0748004\pi\)
\(224\) 19.3138 2.36441i 0.0862223 0.0105554i
\(225\) 0 0
\(226\) −276.951 + 50.8094i −1.22544 + 0.224820i
\(227\) −106.086 + 43.9421i −0.467338 + 0.193578i −0.603910 0.797052i \(-0.706391\pi\)
0.136572 + 0.990630i \(0.456391\pi\)
\(228\) 0 0
\(229\) 46.1162 + 19.1019i 0.201381 + 0.0834146i 0.481094 0.876669i \(-0.340240\pi\)
−0.279714 + 0.960083i \(0.590240\pi\)
\(230\) −19.6322 + 12.6987i −0.0853576 + 0.0552116i
\(231\) 0 0
\(232\) −171.316 + 233.113i −0.738431 + 1.00480i
\(233\) 62.7031 62.7031i 0.269112 0.269112i −0.559630 0.828742i \(-0.689057\pi\)
0.828742 + 0.559630i \(0.189057\pi\)
\(234\) 0 0
\(235\) −19.7247 8.17022i −0.0839347 0.0347669i
\(236\) 0.530099 17.7749i 0.00224618 0.0753175i
\(237\) 0 0
\(238\) −9.39001 + 13.6095i −0.0394538 + 0.0571828i
\(239\) −306.080 −1.28067 −0.640335 0.768095i \(-0.721205\pi\)
−0.640335 + 0.768095i \(0.721205\pi\)
\(240\) 0 0
\(241\) 245.242i 1.01760i 0.860884 + 0.508801i \(0.169911\pi\)
−0.860884 + 0.508801i \(0.830089\pi\)
\(242\) −262.439 + 380.369i −1.08446 + 1.57177i
\(243\) 0 0
\(244\) −25.3268 26.8839i −0.103799 0.110180i
\(245\) −9.11102 + 21.9960i −0.0371878 + 0.0897794i
\(246\) 0 0
\(247\) 138.045 + 138.045i 0.558886 + 0.558886i
\(248\) −168.094 + 101.752i −0.677797 + 0.410290i
\(249\) 0 0
\(250\) 40.9107 26.4621i 0.163643 0.105849i
\(251\) −132.845 + 320.715i −0.529261 + 1.27775i 0.402747 + 0.915311i \(0.368056\pi\)
−0.932008 + 0.362438i \(0.881944\pi\)
\(252\) 0 0
\(253\) −171.461 413.942i −0.677710 1.63614i
\(254\) −322.574 + 59.1796i −1.26998 + 0.232990i
\(255\) 0 0
\(256\) 30.4572 254.182i 0.118973 0.992897i
\(257\) 108.814 0.423399 0.211700 0.977335i \(-0.432100\pi\)
0.211700 + 0.977335i \(0.432100\pi\)
\(258\) 0 0
\(259\) 6.01735 2.49247i 0.0232330 0.00962343i
\(260\) 39.5523 15.0180i 0.152124 0.0577617i
\(261\) 0 0
\(262\) 13.2009 + 20.4087i 0.0503851 + 0.0778958i
\(263\) 150.151 150.151i 0.570916 0.570916i −0.361468 0.932384i \(-0.617724\pi\)
0.932384 + 0.361468i \(0.117724\pi\)
\(264\) 0 0
\(265\) −25.3863 + 25.3863i −0.0957975 + 0.0957975i
\(266\) 2.30436 10.7451i 0.00866301 0.0403952i
\(267\) 0 0
\(268\) 0.945942 0.891155i 0.00352963 0.00332520i
\(269\) 255.485 105.825i 0.949758 0.393403i 0.146618 0.989193i \(-0.453161\pi\)
0.803140 + 0.595791i \(0.203161\pi\)
\(270\) 0 0
\(271\) −261.648 −0.965492 −0.482746 0.875760i \(-0.660361\pi\)
−0.482746 + 0.875760i \(0.660361\pi\)
\(272\) 144.382 + 162.716i 0.530817 + 0.598219i
\(273\) 0 0
\(274\) −49.5839 34.2109i −0.180963 0.124857i
\(275\) 177.789 + 429.220i 0.646504 + 1.56080i
\(276\) 0 0
\(277\) 120.123 290.003i 0.433658 1.04694i −0.544440 0.838799i \(-0.683258\pi\)
0.978098 0.208143i \(-0.0667420\pi\)
\(278\) 70.2848 327.734i 0.252823 1.17890i
\(279\) 0 0
\(280\) −1.91905 1.41032i −0.00685375 0.00503685i
\(281\) −21.7898 21.7898i −0.0775437 0.0775437i 0.667271 0.744815i \(-0.267462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(282\) 0 0
\(283\) −155.937 + 376.466i −0.551016 + 1.33027i 0.365702 + 0.930732i \(0.380829\pi\)
−0.916717 + 0.399537i \(0.869171\pi\)
\(284\) −67.4809 + 150.094i −0.237609 + 0.528501i
\(285\) 0 0
\(286\) 146.295 + 797.420i 0.511520 + 2.78818i
\(287\) 12.4575i 0.0434060i
\(288\) 0 0
\(289\) 104.146 0.360368
\(290\) 34.8266 6.38930i 0.120092 0.0220321i
\(291\) 0 0
\(292\) 158.261 352.012i 0.541990 1.20552i
\(293\) 37.2090 + 15.4125i 0.126993 + 0.0526023i 0.445275 0.895394i \(-0.353106\pi\)
−0.318282 + 0.947996i \(0.603106\pi\)
\(294\) 0 0
\(295\) −1.53903 + 1.53903i −0.00521705 + 0.00521705i
\(296\) −12.9434 84.7072i −0.0437276 0.286173i
\(297\) 0 0
\(298\) 464.637 + 99.6443i 1.55918 + 0.334377i
\(299\) −476.616 197.421i −1.59403 0.660271i
\(300\) 0 0
\(301\) 10.8536 4.49569i 0.0360584 0.0149359i
\(302\) 131.792 191.014i 0.436397 0.632497i
\(303\) 0 0
\(304\) −130.043 63.1915i −0.427772 0.207867i
\(305\) 4.52063i 0.0148217i
\(306\) 0 0
\(307\) −101.089 244.049i −0.329279 0.794949i −0.998646 0.0520174i \(-0.983435\pi\)
0.669368 0.742931i \(-0.266565\pi\)
\(308\) 33.2178 31.2939i 0.107850 0.101603i
\(309\) 0 0
\(310\) 23.5148 + 5.04289i 0.0758541 + 0.0162674i
\(311\) 181.395 + 181.395i 0.583264 + 0.583264i 0.935799 0.352534i \(-0.114680\pi\)
−0.352534 + 0.935799i \(0.614680\pi\)
\(312\) 0 0
\(313\) 110.963 + 110.963i 0.354513 + 0.354513i 0.861786 0.507273i \(-0.169346\pi\)
−0.507273 + 0.861786i \(0.669346\pi\)
\(314\) 232.098 150.127i 0.739166 0.478113i
\(315\) 0 0
\(316\) −253.384 + 96.2102i −0.801850 + 0.304463i
\(317\) −134.161 323.892i −0.423219 1.02174i −0.981392 0.192017i \(-0.938497\pi\)
0.558172 0.829725i \(-0.311503\pi\)
\(318\) 0 0
\(319\) 678.512i 2.12700i
\(320\) −24.0462 + 20.0881i −0.0751443 + 0.0627755i
\(321\) 0 0
\(322\) 5.24020 + 28.5631i 0.0162739 + 0.0887054i
\(323\) 113.508 47.0166i 0.351419 0.145562i
\(324\) 0 0
\(325\) 494.207 + 204.707i 1.52064 + 0.629868i
\(326\) 64.4647 + 99.6629i 0.197744 + 0.305714i
\(327\) 0 0
\(328\) 159.159 + 39.1294i 0.485240 + 0.119297i
\(329\) −18.7502 + 18.7502i −0.0569915 + 0.0569915i
\(330\) 0 0
\(331\) −580.238 240.342i −1.75298 0.726110i −0.997479 0.0709686i \(-0.977391\pi\)
−0.755506 0.655141i \(-0.772609\pi\)
\(332\) −117.551 124.778i −0.354071 0.375839i
\(333\) 0 0
\(334\) 229.849 + 158.587i 0.688171 + 0.474810i
\(335\) −0.159064 −0.000474817
\(336\) 0 0
\(337\) 130.257i 0.386519i 0.981148 + 0.193259i \(0.0619059\pi\)
−0.981148 + 0.193259i \(0.938094\pi\)
\(338\) 490.136 + 338.174i 1.45011 + 1.00051i
\(339\) 0 0
\(340\) 0.793689 26.6135i 0.00233438 0.0782750i
\(341\) −176.361 + 425.772i −0.517187 + 1.24860i
\(342\) 0 0
\(343\) 41.9776 + 41.9776i 0.122384 + 0.122384i
\(344\) −23.3461 152.787i −0.0678666 0.444149i
\(345\) 0 0
\(346\) 7.16277 + 11.0737i 0.0207016 + 0.0320049i
\(347\) 54.6775 132.003i 0.157572 0.380412i −0.825302 0.564692i \(-0.808995\pi\)
0.982874 + 0.184279i \(0.0589951\pi\)
\(348\) 0 0
\(349\) −46.7936 112.970i −0.134079 0.323696i 0.842553 0.538613i \(-0.181052\pi\)
−0.976632 + 0.214918i \(0.931052\pi\)
\(350\) −5.43360 29.6173i −0.0155246 0.0846209i
\(351\) 0 0
\(352\) −295.476 522.689i −0.839420 1.48491i
\(353\) −382.113 −1.08247 −0.541236 0.840871i \(-0.682043\pi\)
−0.541236 + 0.840871i \(0.682043\pi\)
\(354\) 0 0
\(355\) 18.6087 7.70798i 0.0524189 0.0217126i
\(356\) −234.105 105.251i −0.657598 0.295650i
\(357\) 0 0
\(358\) 353.990 228.970i 0.988798 0.639582i
\(359\) 81.2910 81.2910i 0.226437 0.226437i −0.584765 0.811203i \(-0.698813\pi\)
0.811203 + 0.584765i \(0.198813\pi\)
\(360\) 0 0
\(361\) 197.525 197.525i 0.547161 0.547161i
\(362\) −305.308 65.4753i −0.843392 0.180871i
\(363\) 0 0
\(364\) 1.56639 52.5233i 0.00430328 0.144295i
\(365\) −43.6425 + 18.0773i −0.119568 + 0.0495268i
\(366\) 0 0
\(367\) 456.145 1.24290 0.621452 0.783453i \(-0.286543\pi\)
0.621452 + 0.783453i \(0.286543\pi\)
\(368\) 381.385 + 22.7682i 1.03637 + 0.0618701i
\(369\) 0 0
\(370\) −5.95617 + 8.63263i −0.0160977 + 0.0233314i
\(371\) 17.0640 + 41.1963i 0.0459947 + 0.111041i
\(372\) 0 0
\(373\) −184.108 + 444.476i −0.493588 + 1.19163i 0.459294 + 0.888284i \(0.348102\pi\)
−0.952882 + 0.303342i \(0.901898\pi\)
\(374\) 498.871 + 106.986i 1.33388 + 0.286059i
\(375\) 0 0
\(376\) 180.660 + 298.450i 0.480478 + 0.793749i
\(377\) 552.423 + 552.423i 1.46531 + 1.46531i
\(378\) 0 0
\(379\) −108.900 + 262.908i −0.287336 + 0.693690i −0.999969 0.00784682i \(-0.997502\pi\)
0.712634 + 0.701536i \(0.247502\pi\)
\(380\) 6.28165 + 16.5437i 0.0165307 + 0.0435361i
\(381\) 0 0
\(382\) 212.084 38.9090i 0.555194 0.101856i
\(383\) 476.810i 1.24493i 0.782646 + 0.622467i \(0.213869\pi\)
−0.782646 + 0.622467i \(0.786131\pi\)
\(384\) 0 0
\(385\) −5.58569 −0.0145083
\(386\) −63.0957 343.920i −0.163460 0.890985i
\(387\) 0 0
\(388\) 446.169 169.411i 1.14992 0.436625i
\(389\) 71.5472 + 29.6358i 0.183926 + 0.0761846i 0.472746 0.881199i \(-0.343263\pi\)
−0.288820 + 0.957383i \(0.593263\pi\)
\(390\) 0 0
\(391\) −229.570 + 229.570i −0.587136 + 0.587136i
\(392\) 332.816 201.463i 0.849020 0.513936i
\(393\) 0 0
\(394\) −49.2386 + 229.597i −0.124971 + 0.582734i
\(395\) 30.6480 + 12.6948i 0.0775898 + 0.0321388i
\(396\) 0 0
\(397\) 120.360 49.8545i 0.303173 0.125578i −0.225911 0.974148i \(-0.572536\pi\)
0.529084 + 0.848570i \(0.322536\pi\)
\(398\) 443.140 + 305.749i 1.11342 + 0.768212i
\(399\) 0 0
\(400\) −395.461 23.6085i −0.988652 0.0590213i
\(401\) 174.015i 0.433953i −0.976177 0.216976i \(-0.930381\pi\)
0.976177 0.216976i \(-0.0696195\pi\)
\(402\) 0 0
\(403\) 203.063 + 490.237i 0.503878 + 1.21647i
\(404\) 427.534 + 12.7503i 1.05825 + 0.0315601i
\(405\) 0 0
\(406\) 9.22151 42.9995i 0.0227131 0.105910i
\(407\) −142.114 142.114i −0.349173 0.349173i
\(408\) 0 0
\(409\) −108.736 108.736i −0.265857 0.265857i 0.561571 0.827428i \(-0.310197\pi\)
−0.827428 + 0.561571i \(0.810197\pi\)
\(410\) −10.8950 16.8437i −0.0265731 0.0410822i
\(411\) 0 0
\(412\) −296.061 + 658.513i −0.718594 + 1.59833i
\(413\) 1.03450 + 2.49749i 0.00250483 + 0.00604720i
\(414\) 0 0
\(415\) 20.9819i 0.0505589i
\(416\) −666.123 184.989i −1.60126 0.444686i
\(417\) 0 0
\(418\) −333.540 + 61.1913i −0.797942 + 0.146391i
\(419\) −370.373 + 153.414i −0.883946 + 0.366142i −0.778026 0.628232i \(-0.783779\pi\)
−0.105920 + 0.994375i \(0.533779\pi\)
\(420\) 0 0
\(421\) −600.339 248.669i −1.42598 0.590662i −0.469628 0.882864i \(-0.655612\pi\)
−0.956357 + 0.292202i \(0.905612\pi\)
\(422\) −380.342 + 246.016i −0.901284 + 0.582975i
\(423\) 0 0
\(424\) 579.926 88.6135i 1.36775 0.208994i
\(425\) 238.043 238.043i 0.560101 0.560101i
\(426\) 0 0
\(427\) 5.18730 + 2.14865i 0.0121482 + 0.00503197i
\(428\) 410.818 + 12.2518i 0.959856 + 0.0286256i
\(429\) 0 0
\(430\) −10.7432 + 15.5708i −0.0249842 + 0.0362111i
\(431\) −289.906 −0.672636 −0.336318 0.941749i \(-0.609182\pi\)
−0.336318 + 0.941749i \(0.609182\pi\)
\(432\) 0 0
\(433\) 314.414i 0.726129i −0.931764 0.363064i \(-0.881731\pi\)
0.931764 0.363064i \(-0.118269\pi\)
\(434\) 16.9631 24.5857i 0.0390856 0.0566490i
\(435\) 0 0
\(436\) 87.8002 82.7149i 0.201377 0.189713i
\(437\) 82.5760 199.356i 0.188961 0.456192i
\(438\) 0 0
\(439\) −579.455 579.455i −1.31994 1.31994i −0.913818 0.406125i \(-0.866880\pi\)
−0.406125 0.913818i \(-0.633120\pi\)
\(440\) −17.5448 + 71.3634i −0.0398745 + 0.162189i
\(441\) 0 0
\(442\) 493.269 319.060i 1.11599 0.721855i
\(443\) −107.736 + 260.098i −0.243197 + 0.587130i −0.997597 0.0692856i \(-0.977928\pi\)
0.754400 + 0.656415i \(0.227928\pi\)
\(444\) 0 0
\(445\) 12.0223 + 29.0244i 0.0270164 + 0.0652233i
\(446\) 204.280 37.4773i 0.458027 0.0840297i
\(447\) 0 0
\(448\) 11.6215 + 37.1402i 0.0259408 + 0.0829022i
\(449\) −470.997 −1.04899 −0.524496 0.851413i \(-0.675746\pi\)
−0.524496 + 0.851413i \(0.675746\pi\)
\(450\) 0 0
\(451\) 355.147 147.107i 0.787465 0.326179i
\(452\) −199.901 526.471i −0.442260 1.16476i
\(453\) 0 0
\(454\) −124.728 192.830i −0.274730 0.424735i
\(455\) −4.54769 + 4.54769i −0.00999493 + 0.00999493i
\(456\) 0 0
\(457\) 447.868 447.868i 0.980018 0.980018i −0.0197861 0.999804i \(-0.506299\pi\)
0.999804 + 0.0197861i \(0.00629852\pi\)
\(458\) −20.9335 + 97.6121i −0.0457064 + 0.213127i
\(459\) 0 0
\(460\) −32.0657 34.0370i −0.0697080 0.0739935i
\(461\) −253.222 + 104.888i −0.549288 + 0.227523i −0.640027 0.768352i \(-0.721077\pi\)
0.0907394 + 0.995875i \(0.471077\pi\)
\(462\) 0 0
\(463\) −653.753 −1.41199 −0.705996 0.708215i \(-0.749501\pi\)
−0.705996 + 0.708215i \(0.749501\pi\)
\(464\) −520.401 252.877i −1.12155 0.544994i
\(465\) 0 0
\(466\) 145.977 + 100.718i 0.313255 + 0.216133i
\(467\) −39.3875 95.0899i −0.0843416 0.203619i 0.876082 0.482162i \(-0.160148\pi\)
−0.960424 + 0.278544i \(0.910148\pi\)
\(468\) 0 0
\(469\) −0.0756028 + 0.182521i −0.000161200 + 0.000389171i
\(470\) 8.95363 41.7503i 0.0190503 0.0888305i
\(471\) 0 0
\(472\) 35.1576 5.37213i 0.0744865 0.0113816i
\(473\) −256.332 256.332i −0.541927 0.541927i
\(474\) 0 0
\(475\) −85.6236 + 206.714i −0.180260 + 0.435187i
\(476\) −30.1610 13.5601i −0.0633635 0.0284876i
\(477\) 0 0
\(478\) −110.464 602.112i −0.231095 1.25965i
\(479\) 857.713i 1.79063i 0.445432 + 0.895316i \(0.353050\pi\)
−0.445432 + 0.895316i \(0.646950\pi\)
\(480\) 0 0
\(481\) −231.408 −0.481099
\(482\) −482.433 + 88.5072i −1.00090 + 0.183625i
\(483\) 0 0
\(484\) −842.963 378.988i −1.74166 0.783033i
\(485\) −53.9661 22.3535i −0.111270 0.0460897i
\(486\) 0 0
\(487\) 12.5467 12.5467i 0.0257633 0.0257633i −0.694108 0.719871i \(-0.744201\pi\)
0.719871 + 0.694108i \(0.244201\pi\)
\(488\) 43.7448 59.5245i 0.0896410 0.121976i
\(489\) 0 0
\(490\) −46.5579 9.98464i −0.0950161 0.0203768i
\(491\) −91.7015 37.9840i −0.186765 0.0773605i 0.287341 0.957828i \(-0.407229\pi\)
−0.474106 + 0.880468i \(0.657229\pi\)
\(492\) 0 0
\(493\) 454.233 188.149i 0.921365 0.381642i
\(494\) −221.737 + 321.377i −0.448861 + 0.650561i
\(495\) 0 0
\(496\) −260.828 293.947i −0.525862 0.592635i
\(497\) 25.0166i 0.0503352i
\(498\) 0 0
\(499\) 193.677 + 467.577i 0.388130 + 0.937029i 0.990336 + 0.138688i \(0.0442886\pi\)
−0.602206 + 0.798341i \(0.705711\pi\)
\(500\) 66.8201 + 70.9281i 0.133640 + 0.141856i
\(501\) 0 0
\(502\) −678.844 145.582i −1.35228 0.290005i
\(503\) −659.583 659.583i −1.31130 1.31130i −0.920459 0.390840i \(-0.872184\pi\)
−0.390840 0.920459i \(-0.627816\pi\)
\(504\) 0 0
\(505\) −37.0177 37.0177i −0.0733024 0.0733024i
\(506\) 752.415 486.683i 1.48699 0.961823i
\(507\) 0 0
\(508\) −232.832 613.201i −0.458332 1.20709i
\(509\) 133.178 + 321.521i 0.261647 + 0.631671i 0.999041 0.0437918i \(-0.0139438\pi\)
−0.737394 + 0.675463i \(0.763944\pi\)
\(510\) 0 0
\(511\) 58.6707i 0.114815i
\(512\) 511.010 31.8190i 0.998067 0.0621466i
\(513\) 0 0
\(514\) 39.2705 + 214.055i 0.0764018 + 0.416449i
\(515\) 81.6425 33.8174i 0.158529 0.0656649i
\(516\) 0 0
\(517\) 755.957 + 313.127i 1.46220 + 0.605662i
\(518\) 7.07475 + 10.9376i 0.0136578 + 0.0211151i
\(519\) 0 0
\(520\) 43.8173 + 72.3862i 0.0842641 + 0.139204i
\(521\) −71.2918 + 71.2918i −0.136837 + 0.136837i −0.772207 0.635371i \(-0.780847\pi\)
0.635371 + 0.772207i \(0.280847\pi\)
\(522\) 0 0
\(523\) −376.338 155.884i −0.719576 0.298058i −0.00731529 0.999973i \(-0.502329\pi\)
−0.712261 + 0.701915i \(0.752329\pi\)
\(524\) −35.3832 + 33.3338i −0.0675252 + 0.0636142i
\(525\) 0 0
\(526\) 349.562 + 241.183i 0.664566 + 0.458523i
\(527\) 333.940 0.633662
\(528\) 0 0
\(529\) 41.2074i 0.0778968i
\(530\) −59.1011 40.7774i −0.111511 0.0769384i
\(531\) 0 0
\(532\) 21.9691 + 0.655181i 0.0412953 + 0.00123154i
\(533\) 169.379 408.918i 0.317785 0.767201i
\(534\) 0 0
\(535\) −35.5704 35.5704i −0.0664867 0.0664867i
\(536\) 2.09444 + 1.53921i 0.00390754 + 0.00287167i
\(537\) 0 0
\(538\) 300.380 + 464.390i 0.558327 + 0.863178i
\(539\) 349.184 843.005i 0.647837 1.56402i
\(540\) 0 0
\(541\) −131.242 316.846i −0.242591 0.585667i 0.754948 0.655785i \(-0.227662\pi\)
−0.997539 + 0.0701185i \(0.977662\pi\)
\(542\) −94.4281 514.706i −0.174222 0.949643i
\(543\) 0 0
\(544\) −267.982 + 342.748i −0.492614 + 0.630051i
\(545\) −14.7639 −0.0270898
\(546\) 0 0
\(547\) −57.6667 + 23.8863i −0.105424 + 0.0436679i −0.434772 0.900541i \(-0.643171\pi\)
0.329348 + 0.944209i \(0.393171\pi\)
\(548\) 49.4039 109.886i 0.0901531 0.200523i
\(549\) 0 0
\(550\) −780.184 + 504.645i −1.41852 + 0.917536i
\(551\) −231.064 + 231.064i −0.419354 + 0.419354i
\(552\) 0 0
\(553\) 29.1339 29.1339i 0.0526834 0.0526834i
\(554\) 613.837 + 131.641i 1.10801 + 0.237620i
\(555\) 0 0
\(556\) 670.075 + 19.9835i 1.20517 + 0.0359416i
\(557\) −403.952 + 167.322i −0.725228 + 0.300399i −0.714589 0.699544i \(-0.753386\pi\)
−0.0106383 + 0.999943i \(0.503386\pi\)
\(558\) 0 0
\(559\) −417.394 −0.746680
\(560\) 2.08175 4.28408i 0.00371742 0.00765014i
\(561\) 0 0
\(562\) 35.0003 50.7280i 0.0622781 0.0902634i
\(563\) −2.60893 6.29851i −0.00463398 0.0111874i 0.921546 0.388270i \(-0.126927\pi\)
−0.926180 + 0.377083i \(0.876927\pi\)
\(564\) 0 0
\(565\) −26.3767 + 63.6791i −0.0466845 + 0.112706i
\(566\) −796.850 170.890i −1.40786 0.301925i
\(567\) 0 0
\(568\) −319.614 78.5777i −0.562702 0.138341i
\(569\) −225.325 225.325i −0.396002 0.396002i 0.480818 0.876820i \(-0.340340\pi\)
−0.876820 + 0.480818i \(0.840340\pi\)
\(570\) 0 0
\(571\) 203.081 490.280i 0.355658 0.858634i −0.640242 0.768173i \(-0.721166\pi\)
0.995900 0.0904608i \(-0.0288340\pi\)
\(572\) −1515.86 + 575.573i −2.65011 + 1.00625i
\(573\) 0 0
\(574\) −24.5061 + 4.49589i −0.0426935 + 0.00783256i
\(575\) 591.252i 1.02826i
\(576\) 0 0
\(577\) −1017.81 −1.76396 −0.881980 0.471286i \(-0.843790\pi\)
−0.881980 + 0.471286i \(0.843790\pi\)
\(578\) 37.5861 + 204.873i 0.0650278 + 0.354452i
\(579\) 0 0
\(580\) 25.1377 + 66.2040i 0.0433408 + 0.114145i
\(581\) 24.0762 + 9.97270i 0.0414393 + 0.0171647i
\(582\) 0 0
\(583\) 972.943 972.943i 1.66886 1.66886i
\(584\) 749.582 + 184.286i 1.28353 + 0.315558i
\(585\) 0 0
\(586\) −16.8903 + 78.7587i −0.0288230 + 0.134400i
\(587\) 721.215 + 298.737i 1.22865 + 0.508922i 0.900149 0.435583i \(-0.143458\pi\)
0.328498 + 0.944505i \(0.393458\pi\)
\(588\) 0 0
\(589\) −205.053 + 84.9359i −0.348138 + 0.144204i
\(590\) −3.58296 2.47210i −0.00607282 0.00419000i
\(591\) 0 0
\(592\) 161.962 56.0324i 0.273585 0.0946493i
\(593\) 525.499i 0.886170i 0.896479 + 0.443085i \(0.146116\pi\)
−0.896479 + 0.443085i \(0.853884\pi\)
\(594\) 0 0
\(595\) 1.54890 + 3.73937i 0.00260319 + 0.00628465i
\(596\) −28.3311 + 949.980i −0.0475354 + 1.59393i
\(597\) 0 0
\(598\) 216.351 1008.83i 0.361791 1.68701i
\(599\) 359.176 + 359.176i 0.599626 + 0.599626i 0.940213 0.340587i \(-0.110626\pi\)
−0.340587 + 0.940213i \(0.610626\pi\)
\(600\) 0 0
\(601\) 163.858 + 163.858i 0.272642 + 0.272642i 0.830163 0.557521i \(-0.188247\pi\)
−0.557521 + 0.830163i \(0.688247\pi\)
\(602\) 12.7608 + 19.7283i 0.0211974 + 0.0327713i
\(603\) 0 0
\(604\) 423.320 + 190.321i 0.700862 + 0.315101i
\(605\) 43.2897 + 104.511i 0.0715533 + 0.172745i
\(606\) 0 0
\(607\) 208.191i 0.342984i 0.985186 + 0.171492i \(0.0548587\pi\)
−0.985186 + 0.171492i \(0.945141\pi\)
\(608\) 77.3762 278.622i 0.127263 0.458259i
\(609\) 0 0
\(610\) −8.89284 + 1.63148i −0.0145784 + 0.00267456i
\(611\) 870.414 360.537i 1.42457 0.590077i
\(612\) 0 0
\(613\) 643.217 + 266.429i 1.04929 + 0.434632i 0.839640 0.543144i \(-0.182766\pi\)
0.209654 + 0.977776i \(0.432766\pi\)
\(614\) 443.604 286.935i 0.722481 0.467321i
\(615\) 0 0
\(616\) 73.5485 + 54.0511i 0.119397 + 0.0877453i
\(617\) 526.767 526.767i 0.853755 0.853755i −0.136838 0.990593i \(-0.543694\pi\)
0.990593 + 0.136838i \(0.0436941\pi\)
\(618\) 0 0
\(619\) −316.799 131.222i −0.511791 0.211991i 0.111816 0.993729i \(-0.464333\pi\)
−0.623607 + 0.781738i \(0.714333\pi\)
\(620\) −1.43381 + 48.0775i −0.00231259 + 0.0775443i
\(621\) 0 0
\(622\) −291.370 + 422.300i −0.468441 + 0.678939i
\(623\) 39.0188 0.0626306
\(624\) 0 0
\(625\) 607.081i 0.971330i
\(626\) −178.236 + 258.328i −0.284722 + 0.412665i
\(627\) 0 0
\(628\) 379.089 + 402.395i 0.603645 + 0.640757i
\(629\) −55.7309 + 134.546i −0.0886024 + 0.213905i
\(630\) 0 0
\(631\) 515.138 + 515.138i 0.816383 + 0.816383i 0.985582 0.169199i \(-0.0541179\pi\)
−0.169199 + 0.985582i \(0.554118\pi\)
\(632\) −280.707 463.728i −0.444157 0.733747i
\(633\) 0 0
\(634\) 588.732 380.808i 0.928600 0.600644i
\(635\) −30.7220 + 74.1694i −0.0483810 + 0.116802i
\(636\) 0 0
\(637\) −402.053 970.642i −0.631167 1.52377i
\(638\) −1334.75 + 244.873i −2.09208 + 0.383814i
\(639\) 0 0
\(640\) −48.1950 40.0531i −0.0753046 0.0625830i
\(641\) 827.282 1.29061 0.645306 0.763925i \(-0.276730\pi\)
0.645306 + 0.763925i \(0.276730\pi\)
\(642\) 0 0
\(643\) 300.259 124.371i 0.466965 0.193423i −0.136779 0.990602i \(-0.543675\pi\)
0.603744 + 0.797178i \(0.293675\pi\)
\(644\) −54.2974 + 20.6167i −0.0843127 + 0.0320135i
\(645\) 0 0
\(646\) 133.454 + 206.322i 0.206586 + 0.319383i
\(647\) 182.325 182.325i 0.281800 0.281800i −0.552027 0.833827i \(-0.686145\pi\)
0.833827 + 0.552027i \(0.186145\pi\)
\(648\) 0 0
\(649\) 58.9840 58.9840i 0.0908845 0.0908845i
\(650\) −224.336 + 1046.07i −0.345132 + 1.60933i
\(651\) 0 0
\(652\) −172.789 + 162.781i −0.265013 + 0.249664i
\(653\) 83.4520 34.5670i 0.127798 0.0529356i −0.317868 0.948135i \(-0.602967\pi\)
0.445666 + 0.895199i \(0.352967\pi\)
\(654\) 0 0
\(655\) 5.94981 0.00908368
\(656\) −19.5342 + 327.214i −0.0297778 + 0.498801i
\(657\) 0 0
\(658\) −43.6517 30.1179i −0.0663400 0.0457719i
\(659\) −36.4182 87.9213i −0.0552628 0.133416i 0.893837 0.448393i \(-0.148003\pi\)
−0.949099 + 0.314976i \(0.898003\pi\)
\(660\) 0 0
\(661\) −420.501 + 1015.18i −0.636159 + 1.53582i 0.195597 + 0.980684i \(0.437335\pi\)
−0.831757 + 0.555140i \(0.812665\pi\)
\(662\) 263.388 1228.16i 0.397867 1.85523i
\(663\) 0 0
\(664\) 203.036 276.276i 0.305777 0.416078i
\(665\) −1.90218 1.90218i −0.00286042 0.00286042i
\(666\) 0 0
\(667\) 330.450 797.776i 0.495427 1.19607i
\(668\) −229.015 + 509.385i −0.342836 + 0.762553i
\(669\) 0 0
\(670\) −0.0574056 0.312905i −8.56800e−5 0.000467022i
\(671\) 173.255i 0.258205i
\(672\) 0 0
\(673\) 80.3370 0.119372 0.0596858 0.998217i \(-0.480990\pi\)
0.0596858 + 0.998217i \(0.480990\pi\)
\(674\) −256.237 + 47.0094i −0.380174 + 0.0697468i
\(675\) 0 0
\(676\) −488.356 + 1086.23i −0.722421 + 1.60684i
\(677\) 944.061 + 391.043i 1.39448 + 0.577611i 0.948312 0.317339i \(-0.102789\pi\)
0.446165 + 0.894951i \(0.352789\pi\)
\(678\) 0 0
\(679\) −51.3001 + 51.3001i −0.0755524 + 0.0755524i
\(680\) 52.6397 8.04342i 0.0774113 0.0118286i
\(681\) 0 0
\(682\) −901.214 193.271i −1.32143 0.283389i
\(683\) 173.921 + 72.0404i 0.254643 + 0.105476i 0.506353 0.862326i \(-0.330993\pi\)
−0.251711 + 0.967803i \(0.580993\pi\)
\(684\) 0 0
\(685\) −13.6237 + 5.64314i −0.0198887 + 0.00823816i
\(686\) −67.4274 + 97.7266i −0.0982907 + 0.142459i
\(687\) 0 0
\(688\) 292.133 101.066i 0.424612 0.146899i
\(689\) 1584.28i 2.29939i
\(690\) 0 0
\(691\) 185.902 + 448.807i 0.269033 + 0.649503i 0.999438 0.0335109i \(-0.0106688\pi\)
−0.730405 + 0.683014i \(0.760669\pi\)
\(692\) −19.1988 + 18.0868i −0.0277439 + 0.0261370i
\(693\) 0 0
\(694\) 279.405 + 59.9203i 0.402601 + 0.0863404i
\(695\) −58.0179 58.0179i −0.0834790 0.0834790i
\(696\) 0 0
\(697\) −196.962 196.962i −0.282586 0.282586i
\(698\) 205.343 132.821i 0.294188 0.190289i
\(699\) 0 0
\(700\) 56.3013 21.3776i 0.0804304 0.0305395i
\(701\) 150.886 + 364.271i 0.215244 + 0.519645i 0.994214 0.107416i \(-0.0342576\pi\)
−0.778970 + 0.627061i \(0.784258\pi\)
\(702\) 0 0
\(703\) 96.7921i 0.137684i
\(704\) 921.580 769.887i 1.30906 1.09359i
\(705\) 0 0
\(706\) −137.903 751.680i −0.195331 1.06470i
\(707\) −60.0713 + 24.8824i −0.0849665 + 0.0351943i
\(708\) 0 0
\(709\) −457.191 189.375i −0.644839 0.267101i 0.0362043 0.999344i \(-0.488473\pi\)
−0.681043 + 0.732243i \(0.738473\pi\)
\(710\) 21.8787 + 33.8247i 0.0308151 + 0.0476404i
\(711\) 0 0
\(712\) 122.559 498.509i 0.172134 0.700153i
\(713\) 414.720 414.720i 0.581656 0.581656i
\(714\) 0 0
\(715\) 183.350 + 75.9462i 0.256434 + 0.106218i
\(716\) 578.177 + 613.723i 0.807510 + 0.857155i
\(717\) 0 0
\(718\) 189.251 + 130.575i 0.263581 + 0.181860i
\(719\) −1277.00 −1.77608 −0.888039 0.459768i \(-0.847932\pi\)
−0.888039 + 0.459768i \(0.847932\pi\)
\(720\) 0 0
\(721\) 109.756i 0.152227i
\(722\) 459.851 + 317.279i 0.636913 + 0.439444i
\(723\) 0 0
\(724\) 18.6161 624.222i 0.0257128 0.862186i
\(725\) −342.646 + 827.219i −0.472614 + 1.14099i
\(726\) 0 0
\(727\) 470.863 + 470.863i 0.647679 + 0.647679i 0.952432 0.304753i \(-0.0985738\pi\)
−0.304753 + 0.952432i \(0.598574\pi\)
\(728\) 103.888 15.8742i 0.142703 0.0218052i
\(729\) 0 0
\(730\) −51.3115 79.3280i −0.0702898 0.108669i
\(731\) −100.522 + 242.683i −0.137514 + 0.331987i
\(732\) 0 0
\(733\) 364.452 + 879.866i 0.497206 + 1.20036i 0.950982 + 0.309246i \(0.100077\pi\)
−0.453776 + 0.891116i \(0.649923\pi\)
\(734\) 164.622 + 897.315i 0.224280 + 1.22250i
\(735\) 0 0
\(736\) 92.8520 + 758.466i 0.126158 + 1.03052i
\(737\) 6.09619 0.00827163
\(738\) 0 0
\(739\) 1146.65 474.958i 1.55162 0.642704i 0.568016 0.823018i \(-0.307711\pi\)
0.983609 + 0.180314i \(0.0577112\pi\)
\(740\) −19.1314 8.60129i −0.0258533 0.0116234i
\(741\) 0 0
\(742\) −74.8816 + 48.4355i −0.100919 + 0.0652769i
\(743\) −512.021 + 512.021i −0.689126 + 0.689126i −0.962039 0.272913i \(-0.912013\pi\)
0.272913 + 0.962039i \(0.412013\pi\)
\(744\) 0 0
\(745\) 82.2533 82.2533i 0.110407 0.110407i
\(746\) −940.804 201.762i −1.26113 0.270458i
\(747\) 0 0
\(748\) −30.4185 + 1019.97i −0.0406665 + 1.36360i
\(749\) −57.7227 + 23.9095i −0.0770663 + 0.0319219i
\(750\) 0 0
\(751\) 335.629 0.446910 0.223455 0.974714i \(-0.428266\pi\)
0.223455 + 0.974714i \(0.428266\pi\)
\(752\) −521.901 + 463.098i −0.694017 + 0.615822i
\(753\) 0 0
\(754\) −887.341 + 1286.08i −1.17684 + 1.70567i
\(755\) −21.7393 52.4833i −0.0287938 0.0695143i
\(756\) 0 0
\(757\) −139.805 + 337.518i −0.184682 + 0.445863i −0.988921 0.148444i \(-0.952573\pi\)
0.804238 + 0.594307i \(0.202573\pi\)
\(758\) −556.487 119.342i −0.734152 0.157444i
\(759\) 0 0
\(760\) −30.2772 + 18.3276i −0.0398385 + 0.0241153i
\(761\) −495.581 495.581i −0.651223 0.651223i 0.302064 0.953288i \(-0.402324\pi\)
−0.953288 + 0.302064i \(0.902324\pi\)
\(762\) 0 0
\(763\) −7.01728 + 16.9412i −0.00919696 + 0.0222034i
\(764\) 153.081 + 403.163i 0.200368 + 0.527700i
\(765\) 0 0
\(766\) −937.965 + 172.079i −1.22450 + 0.224647i
\(767\) 96.0458i 0.125223i
\(768\) 0 0
\(769\) 372.267 0.484092 0.242046 0.970265i \(-0.422181\pi\)
0.242046 + 0.970265i \(0.422181\pi\)
\(770\) −2.01586 10.9880i −0.00261800 0.0142701i
\(771\) 0 0
\(772\) 653.778 248.240i 0.846862 0.321554i
\(773\) 534.778 + 221.512i 0.691822 + 0.286562i 0.700759 0.713398i \(-0.252845\pi\)
−0.00893708 + 0.999960i \(0.502845\pi\)
\(774\) 0 0
\(775\) −430.026 + 430.026i −0.554873 + 0.554873i
\(776\) 494.280 + 816.550i 0.636959 + 1.05226i
\(777\) 0 0
\(778\) −32.4775 + 151.441i −0.0417448 + 0.194654i
\(779\) 171.040 + 70.8470i 0.219563 + 0.0909461i
\(780\) 0 0
\(781\) −713.187 + 295.412i −0.913172 + 0.378248i
\(782\) −534.455 368.752i −0.683446 0.471550i
\(783\) 0 0
\(784\) 516.424 + 581.998i 0.658704 + 0.742344i
\(785\) 67.6643i 0.0861965i
\(786\) 0 0
\(787\) −280.233 676.541i −0.356077 0.859646i −0.995844 0.0910769i \(-0.970969\pi\)